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((3*x+5)*tan(x))

Derivative of ((3*x+5)*tan(x))

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

You have entered [src]
(3*x + 5)*tan(x)
$$\left(3 x + 5\right) \tan{\left(x \right)}$$
(3*x + 5)*tan(x)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Differentiate term by term:

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      2. The derivative of the constant is zero.

      The result is:

    ; to find :

    1. Rewrite the function to be differentiated:

    2. Apply the quotient rule, which is:

      and .

      To find :

      1. The derivative of sine is cosine:

      To find :

      1. The derivative of cosine is negative sine:

      Now plug in to the quotient rule:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
           /       2   \          
3*tan(x) + \1 + tan (x)/*(3*x + 5)
$$\left(3 x + 5\right) \left(\tan^{2}{\left(x \right)} + 1\right) + 3 \tan{\left(x \right)}$$
The second derivative [src]
  /         2      /       2   \                 \
2*\3 + 3*tan (x) + \1 + tan (x)/*(5 + 3*x)*tan(x)/
$$2 \left(\left(3 x + 5\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 3 \tan^{2}{\left(x \right)} + 3\right)$$
The third derivative [src]
  /       2   \ /           /         2   \          \
2*\1 + tan (x)/*\9*tan(x) + \1 + 3*tan (x)/*(5 + 3*x)/
$$2 \left(\left(3 x + 5\right) \left(3 \tan^{2}{\left(x \right)} + 1\right) + 9 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)$$
The graph
Derivative of ((3*x+5)*tan(x))